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                        DIAMOND OFFSHORE DRILLING, INC.
                                  ("COMPANY")

                                DEBT SECURITIES

                                TERMS AGREEMENT


                                                                January 29, 1997


To:  The Underwriters identified herein



Dear Sirs:

         The undersigned agrees to sell to the several Underwriters named in
Schedule A hereto for their respective accounts, on and subject to the terms
and conditions of the Underwriting Agreement incorporated by reference in the
Company's registration statement on Form S-3 (No. 333-19987) ("Underwriting
Agreement"), the following securities ("Offered Securities") on the following
terms:
            
         TITLE:  3 3/4% Convertible Subordinated Notes Due 2007.

         PRINCIPAL AMOUNT OF FIRM SECURITIES:  $350,000,000.

         PRINCIPAL AMOUNT OF OPTIONAL SECURITIES:  $50,000,000.

         TERM OF OVER-ALLOTMENT OPTION:    30 days from the date of this 
agreement.

         INTEREST:      3 3/4% per annum, from February 4, 1997 , payable
semiannually on February 15 and August 15 of each year, commencing August 15,
1997, to holders of record on the preceding February 1 or August 1, as the case
may be.

         MATURITY:  February 15, 2007.

         OPTIONAL REDEMPTION:  The Notes may be redeemed at the option of the
Company, at any time and from time to time, in whole or in part, on at least 30
and not more than 60 days' notice by mail to the registered Holders thereof, at
any time on or after February 22, 2001 and prior to February 15, 2002 at
102.08% of principal amount and, thereafter, at the following redemption prices
(expressed as percentages of principal amount), if redeemed during the 12-month
period beginning on February 15 of the years set forth below:



    YEAR                               PERCENTAGE
     ----                               ----------
                                      
     2002  . . . . . . . . . . . . .     101.67%
     2003  . . . . . . . . . . . . .     101.25%
     2004  . . . . . . . . . . . . .     100.83%
     2005  . . . . . . . . . . . . .     100.42%


and thereafter at 100% of the principal amount thereof; in each case together
with accrued and unpaid interest to (but not including) the redemption date
(subject to the rights of holders on any regular record date to receive
interest due on any interest payment date that is on or prior to such
redemption date).
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         SINKING FUND:  None.

         LISTING:  None.

         DELAYED DELIVERY CONTRACTS:  None.

         PURCHASE PRICE:  98.75 % of principal amount, plus accrued interest, 
if any, from February 4, 1997.

         CONVERSION PRICE:  The Notes are convertible into shares of Common
Stock of the Company, par value $0.01 per share, at a conversion price of
$81.00 per share (equivalent to a conversion rate of 12.346 shares per $1,000
principal amount of Notes), subject to adjustment in certain circumstances.

         EXPECTED REOFFERING PRICE:     100.0% of principal amount, subject to
change by the Underwriters.

         CLOSING:    9:00 A.M. on February 4, 1997, at  the offices of Andrews
& Kurth L.L.P., 425 Lexington Avenue, 10th Floor, New York, New York  10017, in
Federal (same day) funds.

         SETTLEMENT AND TRADING:  Book-Entry Only via DTC.  The Offered
Securities will trade in DTC's Same Day Funds Settlement System.

         BLACKOUT:  Until 90 days after the First Closing Date.

         NAME AND ADDRESS OF REPRESENTATIVE:

         Credit Suissee First Boston Corporation, 11 Madison Avenue, New York,
New York  10010-3629

         The respective principal amounts of the Offered Securities to be
purchased by each of the Underwriters are set forth opposite their names in
Schedule A hereto.

         The provisions of the Underwriting Agreement are incorporated herein
by reference.

         The Offered Securities will be made available for checking and packing
at the office of the Trustee at least 24 hours prior to the Closing Date.

         For purposes of Section 6 of the Underwriting Agreement, the only
information furnished to the Company by any Underwriter for use in the
Prospectus consists of (i) the following information in the Prospectus
furnished on behalf of each Underwriter: the last paragraph at the bottom of
the prospectus supplement cover page concerning the terms of the offering by
the Underwriters, the legend concerning over-allotments and stabilizing on the
inside front cover page of the prospectus supplement, the concession and
reallowance figures appearing in the fourth paragraph under the caption
"Underwriting" in the prospectus supplement and (ii) the following information
in the prospectus supplement furnished on behalf of Merrill Lynch & Co.,
Merrill Lynch, Pierce Fenner & Smith Incorporated:  the third legend on the
inside front cover page and the last paragraph under the caption "Underwriting"
concerning Merrill Lynch Specialists Inc. acting as a specialist.





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If the foregoing is in accordance with your understanding of our agreement,
kindly sign and return to the Company one of the counterparts hereof, whereupon
it will become a binding agreement between the Company and the several
Underwriters in accordance with its terms.

                                 Yours  very truly,

                                 DIAMOND OFFSHORE DRILLING, INC.


                                 By   /s/ Robert E. Rose
                                 --------------------
                                 Name:  Robert E. Rose
                                 Title:  President and Chief Executive Officer


The foregoing Terms Agreement is hereby confirmed and accepted as of the date
first above written.


    CREDIT SUISSE FIRST BOSTON CORPORATION


         By  /s/Rome Arnold             
           ---------------------             
             Name:  Rome Arnold
             Title:  Managing Director

         Acting on behalf of itself and as the Representative of the several
         Underwriters.


                                                     


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                                                                      SCHEDULE A




                                                                               PRINCIPAL
                          UNDERWRITER                                            AMOUNT
                          -----------                                            ------
                                                                           
 Credit Suisse First Boston Corporation  . . . . . . . . . . . . . . . . .    $116,668,000
 Merrill Lynch, Pierce, Fenner & Smith Incorporated  . . . . . . . . . . .    $116,666,000
 Salomon Brothers Inc  . . . . . . . . . . . . . . . . . . . . . . . . . .    $116,666,000
                                                                              ------------
        Total. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .    $350,000,000
                                                                              ============






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                                   ANNEX I

                             LIST OF SUBSIDIARIES
                                                                
                                                                   INCORPORATION
SUBSIDIARY                                                         STATE/COUNTRY
- ----------                                                         -------------
Diamond Offshore Company                                           De
Diamond Offshore General Company                                   De
Diamond Offshore Guardian Company                                  De
Diamond Offshore Southern Company                                  De
Diamond Offshore Management Company                                De
Diamond Offshore (USA) Inc.                                        De
Diamond Offshore Alaska, Inc.                                      De
Diamond Offshore Atlantic, Inc.                                    De
Diamond Offshore (Mexico) Company                                  De
Diamond Offshore Drilling Services, Inc.                           De
Diamond Offshore International Corporation                         De
Diamond Offshore Enterprises, Inc.                                 De
Cumberland Maritime Corporation                                    De
Diamond Offshore Turnkey Services, Inc.                            De
Diamond Offshore Finance Company                                   De
Diamond Offshore Perforadora, Inc.                                 De
Diamond Offshore Limited                                           England
Diamond Offshore Drilling (UK), Limited                            England
Diamond Offshore Development Company                               De
Diamond Offshore (Indonesia) Inc.                                  De
Diamond Offshore Drilling (Overseas) Inc.                          De
Diamond Offshore Exploration (Bermuda) Limited                     De
Arethusa Off-Shore Company                                         De
Concord Drilling Limited                                           De
Saratoga Drilling Limited                                          De
Yorktown Drilling Limited                                          De
Scotian Drilling Limited                                           De
Heritage Drilling Limited                                          De
Sovereign Drilling Limited                                         De
Miss Kitty Drilling Limited                                        De
Neptune Drilling Limited                                           De
Whittington Drilling Limited                                       De
Yatzy Drilling Limited                                             De
Winner Drilling Limited                                            De
Lexington Drilling Limited                                         De






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